This activity involves rounding four-digit numbers to the nearest thousand.
What happens when you round these three-digit numbers to the nearest 100?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
What happens when you round these numbers to the nearest whole number?
Find the sum of all three-digit numbers each of whose digits is
In this problem we are looking at sets of parallel sticks that
cross each other. What is the least number of crossings you can
make? And the greatest?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Delight your friends with this cunning trick! Can you explain how
Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.
Are these statements relating to odd and even numbers always true, sometimes true or never true?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?
Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?
Can you explain how this card trick works?
This challenge asks you to imagine a snake coiling on itself.
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
Can you dissect an equilateral triangle into 6 smaller ones? What
number of smaller equilateral triangles is it NOT possible to
dissect a larger equilateral triangle into?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Here are two kinds of spirals for you to explore. What do you notice?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.
If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable.
Decide which of these diagrams are traversable.
Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
How could Penny, Tom and Matthew work out how many chocolates there
are in different sized boxes?
Consider all two digit numbers (10, 11, . . . ,99). In writing down
all these numbers, which digits occur least often, and which occur
most often ? What about three digit numbers, four digit numbers. . . .
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Imagine starting with one yellow cube and covering it all over with
a single layer of red cubes, and then covering that cube with a
layer of blue cubes. How many red and blue cubes would you need?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
How many centimetres of rope will I need to make another mat just
like the one I have here?
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
An investigation that gives you the opportunity to make and justify
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?